If you navigate from one html file to another, I don't think there is a simple way except local storage or similar API, or cookies.
If you don't want to use one of these especially because the data stay stored even after you leave the page, think about having multiple pages in html document and submitting the form using ajax instead and after the data are submitted, changing the page programatically using $.mobile.changePage("#resultPage");
There is a plugin for submitting the form using ajax here: http://jquery.malsup.com/form/
Then it shoud be easy to pick the data from a local variable.
Edit:
Check the answer here. There is apparently a way how to store data unique for a particular browser window (so it does not remain stored after you leave). But I guess doing things the recommended way is usually best thing to do.
can JavaScript store data unique to a particular browser window instance?